Problem: Solve for $x$ and $y$ using substitution. ${-6x+2y = 6}$ ${y = -4x+10}$
Since $y$ has already been solved for, substitute $-4x+10$ for $y$ in the first equation. ${-6x + 2}{(-4x+10)}{= 6}$ Simplify and solve for $x$ $-6x-8x + 20 = 6$ $-14x+20 = 6$ $-14x+20{-20} = 6{-20}$ $-14x = -14$ $\dfrac{-14x}{{-14}} = \dfrac{-14}{{-14}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -4x+10}\thinspace$ to find $y$ ${y = -4}{(1)}{ + 10}$ $y = -4 + 10$ $y = 6$ You can also plug ${x = 1}$ into $\thinspace {-6x+2y = 6}\thinspace$ and get the same answer for $y$ : ${-6}{(1)}{ + 2y = 6}$ ${y = 6}$